(1/2.5)+ (1/5.8)+ (1/8.11)+.......upto n terms =

Question

(1/2.5)+ (1/5.8)+ (1/8.11)+.......upto n terms = (A)  (n/4n+6) (B)  (1/6n+4) (C)  (n/6n+4) (D)  (n/3n+7)

Tardigrade Admin · Accepted Answer

Let Sn=(1/2 ⋅ 5)+(1/5 ⋅ 8)+(1/8 ⋅ 11)+ ldots+(1/(3 n-1)(3 n+2)) =(1/3)[(1/2)-(1/5)+(1/5)-(1/8)+ ldots ldots ldots+(1/3 n-1)-(1/3 n+2)] =(1/3)[(1/2)-(1/3 n+2)] =(n/6 n+4)

Q. $\frac{1}{2.5} + \frac{1}{5.8} + \frac{1}{8.11}$ +.......upto $n$ terms =

$\frac{n}{4 n + 6}$

$\frac{1}{6 n + 4}$

$\frac{n}{6 n + 4}$

$\frac{n}{3 n + 7}$

Q. 2.51​+5.81​+8.111​+.......upto n terms =

4n+6n​

6n+41​

6n+4n​

3n+7n​

Let Sn​=2⋅51​+5⋅81​+8⋅111​+…+(3n−1)(3n+2)1​ =31​[21​−51​+51​−81​+………+3n−11​−3n+21​] =31​[21​−3n+21​] =6n+4n​

Q. $\frac{1}{2.5} + \frac{1}{5.8} + \frac{1}{8.11}$ +.......upto $n$ terms =

$\frac{n}{4 n + 6}$

$\frac{1}{6 n + 4}$

$\frac{n}{6 n + 4}$

$\frac{n}{3 n + 7}$